Can Polar Interface Energies be Calculated by Means of Supercells?
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CAN POLAR INTERFACE ENERGIES BE CALCULATED BY MEANS OF SUPERCELLS? W. R. L. LAMBRECHT, C. AMADOR and B. SEGALL Department of Physics, Case Western Reserve University, Cleveland, OH 44106-7079 ABSTRACT Two problems associated with the calculation of polar interface energies in semiconductors or insulators are discussed: (1) the stoichiometry of the associated interface region, and (2) the impossibility of constructing a supercell with two equivalent interfaces in certain cases. An approach for calculating the energy of a single interface is introduced. It utilizes local quantities obtained from supercell calcualtions and the electrostatic energy of the isolated single interface. Results are presented for GaAs inversion domain boundaries and NaCl antiphase boundaries. The problem associated with charge transfer between two different interfaces is discussed. INTRODUCTION The most frequently used approach to describe defects in solids and/or interfaces between two solids employs supercells. In this method, one studies a model system with artificially introduced periodic boundary conditions. This allows one to use the standard band-structure methods because the electronic structure problem is reduced to that of a crystal with a large unit cell. Although in this way one introduces spurious defect interaction effects, these can be minimized by choosing sufficiently large supercells. This approach is very useful in practice, because total energy differences tend to be well described with fairly small supercells. Typically, a few layers of each material are sufficient for an interface calculation. Nevertheless, there are certain interface problems which cannot be addressed by means of this approach. The reason for this is that in a supercell description of an interface system, there are, in general, two different interfaces. One can thus not obtain the interface energy as the difference between the supercell and the corresponding bulk energy, but only the sum of the two different interface energies. One can, of course, always calculate the electronic structure and even local changes in total energy due to relaxation, but not the absolute value of the interface energy. In the present paper, we present a new approach, which allows us to solve this problem. Below, we first discuss the definition of the interface energy in the Gibbs sense [1] and show that there is a problem with polar interfaces related to the definition of the stoichiometry and the choice of the interface region. By polar interfaces are meant interfaces along crystallographic planes which are not neutral in the bulk solid because they do not contain an equal number of cations and anions. Next, we introduce our new approach, which is based on the use of a cellular band-structure method such as the linear-muffin-tin orbital (LMTO) method in the atomic-sphere-approximation (ASA) [2]. In this sense, the method is closely related to multiple scattering techniques. The division of the total energy in local intra-cellular terms and inter-cellular interactions is wha
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